The history of rock ’n’ roll is full of extravagant tales told by unreliable narrators, but “Lambert & Stamp” isn’t one of them. James D. Cooper’s documentary about the creation of The Who never lacks for extravagance—the film looks as striking as it sounds—and some of the tales certainly seem outlandish. Yet they’re part of a truly remarkable origin story that the film and its subjects explore with uncommon thoughtfulness and depth of feeling.

The cast of characters sitting for Mr. Cooper’s camera includes two of the...